DUALITY OF WAVE PACKETS AND SOLITARY WAVES IN ABSORPTIVE SYSTEMS.

Unlike the approach of investigating solitary waves by solving certain integrable nonlinear differential equations, which is limited to physical systems described by these equations, the present treatment is based on the duality of wave packets and localized pulses. This approach facilitates the study of non-integrable systems which admit solitary waves as an approximate and transient solution, without reference to specific differential equations. The method has been previously introduced for studying linear and nonlinear lossless systems. Corresponding to the Hamilton ray equations for wave packets in dispersive weakly inhomogeneous media, dual ray equations have been derived describing the behavior of solitary waves in inhomogeneous weakly dispersive media. Exploiting the duality properties the mathematical description of solitary waves in absorbing media is obtained. The physical meaning of the theoretical absorption model is investigated. It is shown that for wave packets the spectrum is broadened as a result of absorption. For solitary waves, the effect of absorption is to produce fission, such that the localized pulse nature is obliterated. The formal extension of the dual ray equations for absorbing media is presented. Finally, simple examples are provided, based on appropriate modification of canonical equations, e. g. , the Korteveg de Vries equation.